Let X₁, X2, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected and variances o,o2, and o3, respectively values M1, M₂₂ a) If μ = μ₂=₂= 60 and o² = 0² = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 < X < 62), where and | Из
Let X₁, X2, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected and variances o,o2, and o3, respectively values M1, M₂₂ a) If μ = μ₂=₂= 60 and o² = 0² = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 < X < 62), where and | Из
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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Only need answer for question d)
![1. Let X₁, X2, and X3 represent the times necessary to perform three successive repairs tasks at a
certain service facility. Suppose they are independent, normal random variables with expected
values µ‚ µ², and µ and variances σ²,02, and o3, respectively
a) If μ₁ = μ₂ = μ₂ = 60 and σ² = 0² = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200).
b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), where
X₁ + X₂ + X3
1
2
3
c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ – 0.5X₂ – 0.5X3 ≤5).
d) If μ = 40, μ₂ = 50, µ = 60, o² =10, o² = 12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).
X
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F121a245b-4265-470c-906a-aeb7dc29a223%2F221f8c3d-0973-4ec3-93f5-05bebbefb34c%2F5a14psp_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let X₁, X2, and X3 represent the times necessary to perform three successive repairs tasks at a
certain service facility. Suppose they are independent, normal random variables with expected
values µ‚ µ², and µ and variances σ²,02, and o3, respectively
a) If μ₁ = μ₂ = μ₂ = 60 and σ² = 0² = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200).
b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), where
X₁ + X₂ + X3
1
2
3
c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ – 0.5X₂ – 0.5X3 ≤5).
d) If μ = 40, μ₂ = 50, µ = 60, o² =10, o² = 12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).
X
=
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